Acronym	tosquat
Name	truncated square tiling
	©
Vertex figure	[4,82]
External links

As abstract polytope tosquat is isomorphic to quitsquat, thereby replacing octagons by octagrams.

Incidence matrix according to Dynkin symbol

x4x4o   (N → ∞)

. . . | 4N |  1  2 | 2 1
------+----+-------+----
x . . |  2 | 2N  * | 2 0
. x . |  2 |  * 4N | 1 1
------+----+-------+----
x4x . |  8 |  4  4 | N *
. x4o |  4 |  0  4 | * N

snubbed forms: s4x4o, x4s4o, s4s4o

x4x4x   (N → ∞)

. . . | 8N |  1  1  1 | 1  1 1
------+----+----------+-------
x . . |  2 | 4N  *  * | 1  1 0
. x . |  2 |  * 4N  * | 1  0 1
. . x |  2 |  *  * 4N | 0  1 1
------+----+----------+-------
x4x . |  8 |  4  4  0 | N  * *
x . x |  4 |  2  0  2 | * 2N *
. x4x |  8 |  0  4  4 | *  * N

snubbed forms: s4x4x, x4s4x, s4s4x, s4x4s, s4s4s

x4x4/3o   (N → ∞)

. .   . | 4N |  1  2 | 2 1
--------+----+-------+----
x .   . |  2 | 2N  * | 2 0
. x   . |  2 |  * 4N | 1 1
--------+----+-------+----
x4x   . |  8 |  4  4 | N *
. x4/3o |  4 |  0  4 | * N

s4o4x   (N → ∞)

demi( . . . ) | 4N |  1  2 | 1 2
--------------+----+-------+----
      s4o .   |  2 | 2N  * | 0 2
demi( . . x ) |  2 |  * 4N | 1 1
--------------+----+-------+----
demi( . o4x ) |  4 |  0  4 | N *
sefa( s4o4x ) |  8 |  4  4 | * N

starting figure: x4o4x
snubbed forms: s4o4s', ss'4o4x

s4x4x   (N → ∞)

demi( . . . ) | 8N |  1  1  1 |  1 1 1
--------------+----+----------+-------
demi( . x . ) |  2 | 4N  *  * |  1 1 0
demi( . . x ) |  2 |  * 4N  * |  0 1 1
sefa( s4x . ) |  2 |  *  * 4N |  1 0 1
--------------+----+----------+-------
      s4x .   ♦  4 |  2  0  2 | 2N * *
demi( . x4x ) |  8 |  4  4  0 |  * N *
sefa( s4x4x ) |  8 |  0  4  4 |  * * N

starting figure: x4x4x
snubbed forms: s4x4s'

:wxw:∞:oqo:&##x   (N → ∞)   → height(1,2) = height(2,3) = 1/sqrt(2) = 0.707107
                              height(3,1') = 1

 o.. ∞ o..      | N  * * |  2 1 0  0 | 2 1
 .o. ∞ .o.      | * 2N * |  1 0 1  1 | 2 1
 ..o ∞ ..o      | *  * N |  0 1 0  2 | 2 1
----------------+--------+-----------+----
 oo. ∞ oo. &#x  | 1  1 0 | 2N * *  * | 1 1
:o.o:∞:o.o:&#x  | 1  0 1 |  * N *  * | 2 0
 .x.   ...      | 0  2 0 |  * * N  * | 2 0
 .oo ∞ .oo &#x  | 0  1 1 |  * * * 2N | 1 1
----------------+--------+-----------+----
:wxw:  ... &#xt | 2  4 2 |  2 2 2  2 | N *
 ...   oqo &#xt | 1  2 1 |  2 0 0  2 | * N